The most fundamental laws of nature are not Newton's or Einstein's laws. The most fundamental laws of nature are the thermodynamic laws of energy conservation and entropy. Everything else is a consequence of these, says Erik Verlinde in this interview.

The Dutch physicist and string theorist Erik Verlinde made quite an impression when he published a paper a little years ago in which he tried to explain how gravity, particles and even space itself can emerge from an entropic force. According to him, these phenomena are not fundamental things, but macroscopic effects of an underlying structure that is out of thermodynamic equilibrium.

Since Verlinde, working at the University of Amsterdam, published his ideas on arXiv.org in January, interest has grown among colleagues. Some have tried to carry further his ideas, others have been doubtful. Most have been cautiously positive because Mr. Verlinde is no Mr anybody in the circles of physicists. He has made important contributions to field theory and is known as a capable string theorist. Therefore, many theoretical physicists are now waiting for his next step, hopefully in the form of a more comprehensive paper before at the end of this year.

If Verlinde's ideas prove to be fruitful, theoretical physics and cosmology as we know it will surely be facing a grand paradigm shift. The universe will no longer be seen as a half-empty container harboring a few particles and forces, but rather as a stretched spaghetti or an amorphous sponge, trying to regain its equilibrium. According to Verlinde, it will become possible to explain dark energy and dark matter out of general principles and we would have to realize that entropy is the reason why large and small forces of nature act the way they do.

"My basic starting point is that the laws of physics that we use now in our descriptions of nature, are actually derived from something else," says Verlinde in this interview.

"If you start from a system, which you don’t really know what is, just be general principles, you can still try to get a lot of information about it by probing it with some external parameters. Actually, the things we use in physics, like positions of particles, even the idea of a particle, or where matter is located – all those things are basically things we have introduced to describe nature, but indeed are more like macroscopic parameters by which we probe that system."

Verlinde's general principle is this: If you change these parameters in such a way that something happens to the amount of its information – a more precise way would be to say with the phase space associated with the system - then you will generate a force. Just by general principles.

“Our world, even spacetime and everything like that, eventually emerges from something, which has a underlying description, which has a lot of information associated to that. A priori you don’t need mass, but of course, if you have a mass present, for instance in the form of a particle, things we observe as energy, then of course there is more information present. So there is actually a measure of information, which you can associate with that."

Nothing mysterious about entropy
This measure of information is entropy, which is basically the information we are not seeing. When a physical system maximizes its entropy it just means that we have to expect the worst of our state of knowledge. If we don’t know the dynamics and the dynamics is very complicated, then we have to guess, and usually it is a good thing to guess the most probable state. Entropy by definition measures the probability, so the highest entropy just means the most probable.

"Since Einstein we have this very sharp separation between what spacetime is, which is sort of like a scene, on which particles can move. This is even what Newton had – well Newton had space and time separate and Einstein put that together. What Einstein showed is that space and time curve. And if you look at the mathematics he used, it looks very much alike the mathematics used for elasticity. It is precisely how you deform material objects. So the terminology he used – like energy and so on – is sometimes called stress which is sort of what you put into material. I think indeed what we are learning now, and I think my idea will lead to that, is that the distinction between what we call space and time and what matter is, starts to become more vague and eventually be manifestations of the same thing."

The first principles by which Verlinde expands his argument are to assume that there is something microscopically there, look at its phase space, that is the space of velocity (momentum) and positions, and apply an adiabatic argument.

“There is one thing I use which is called adiabatic invariance, which is, when you influence a system, you can get the reaction forced back on you. The most simple example would be if you take a harmonic oscillator which swings back and forth in a certain frequency. If you would change the frequency with an external parameter, very slowly, you will need a force to do that. What stays constant is not the energy but the volume of the phase space. It is some invariant you can use. In quantum mechanics it corresponds to letting the quantum state of the system really be the same state, but you change the frequency that means that the energy of the quantum state will change and this is what creates the back reaction. So this is exactly what happens with this atomic model. There is a general notion saying that if you influence a system of fast variables, using some slow variables, then the fast variables react back onto the slow ones. “

“Our world is made out of slow control parameters where we feel the reaction forces, i.e. the back reaction of other degrees of freedom that we are influencing when we change things. Then: how do you calculate those forces? Well, it can be very complicated. We have very little information about what is happening in this microscopic world. Then there is this principle, which tells you that if you just look at the volume of phase space, and how that is changed when you change the parameter, from that you can deduce what the force looks like. And the volume is what I call the entropy. It is the amount of information that is there. The general principle is that if you change the amount of information then there is a cost that you need to pay and that cost can be expressed as a temperature and then the back reaction as a result of that is the force that we see as gravity."

"So we have a general understanding that says that if you affect a system of fast variables by using the slow variable, then the fast variables respond back and generate a force. Our world is made of slow control parameters, where we feel the reactive forces - ie. the backlash of other degrees of freedom that we affect when we change things. The question then is: How do you calculate these forces? It can quickly become very complicated. We have very little information about what happens at this microscopic level and fast. Fortunately, there is a principle that tells us how these forces seem just by looking at the change of system volume in phase space. "

The holographic principle
This principle is called the holographic principle and is basically the idea that the maximum amount of information that can be put into a given region of space can be achieved by placing a black hole in it. And then the amount of information is proportional to the area of the surface around it. Some people say that it means, basically, everything that goes on inside that part of space can be mapped onto bits on the boundary. In Hollywood terms, this principle is formulated as 'everything can be projected onto a screen'.

“It tells you that if you just look at the volume of phase space, and how that is changed when you change the parameter, from that you can deduce what the force looks like. And the volume is what I call the entropy. It is the amount of information, that is there. The general principle then, is that if you change the amount of information then there is a cost that you need to pay and that cost can be expressed as a temperature and then the back reaction as a result of that is the force that we see as gravity.”

So what physicists normally call a graviton is from your perspective an emergent phenomenon on a macroscopic level, right?
“Yes. We have not seen gravitons. We havn't even seen gravitational waves. Of course, most physicists, including me, believe that these things do exist in some form. But the analogy I like to make here is that even if we have an understanding of a solid in terms of an atom, you can also think of a sound wave go through it. If you quantize them you have phonons which is a very useful concept, because they are one way to think of a sound waves through a solid.

They are only an abstraction of the sound?
“Yes, if you quantize sound, you really think of particles with the same properties as photons that only transfer a certain amount of energy and so on. They have particle-like properties, but of course, when I think about sound waves going through a material, I don't think of particles.”

You wrote: if the universe would be energetically in equilibrium, everything would be one giant black hole. How does that work?
“Well, we live in a world that has a cosmological constant. If you only would have a cosmological constant, then the universe would look like what's called de Sitter space. It means that the universe has a horizon, just like black holes. When we look out into space, we see that things move away from us. They are redshifted, meaning that their colours change. And there is a certain distance, which we call the horizon, where the colours really disappear and fade out and become sort of black. You can thus think of the universe being a black hole.”

Isn't this just a function of our ability to see as far as possible?
“No, and in a certain way yes. In the way we use Einstein's equations there is really something what's called a horizon, very analogous to what a horizon of a black hole is. It is a place where the redshifts of a signal go to zero, or infinity, however you want to measure it. Everything slows down and you don't see any light coming from there any more.”

How does this relate to the big bang?
“I think that my ideas eventually will do is to change our understanding what a big bang really means, and whether there really was a big bang.”

How do you mean that?
“Well, part of my work still isn't finished, but I can tell you a little bit of what I have in mind. What I see is that... actually its the way I understand how matter can form from a black hole, or indeed how it can emerge from this de Sitter horizon. There is a lot of.. I don't want to call it matter, so let's call it 'stuff'... There is something there which is in equilibrium and then there are certain things which get out of equilibrium. Those are the things that we eventually will see as matter. So the matter that we see in the universe is actually an exception – it is the stuff that is out of equilibrium while most of it is in equilibrium. This is an idea which eventually will lead me to describing what is dark energy and dark matter – and ordinary matter. I believe that the dark energy is the stuff that is much closer to equilibrium, dark matter is a little further out of equilibrium, and the rest if the visible matter is even further out. So, normal matter is really the most out of equilibrium.”

A bit of odd numerologyIs there anything that is even further away from equilibrium than the visible matter?
“Yes, that's radiation. In fact the funny thing, and an amusing numerology, is that if you take a gaussian distribution, a bell curve, then you have something called sigma, the width of the Gaussian. If you take one sigma as dark energy and two sigma as dark matter and anything beyond as ordinary matter, you are getting pretty close to what's being observed. We have around 68% covered by the first sigma, 96% gets you two sigma, but of course the difference is something like 28 %, and then there are four percent left for the rest. The fit that people make is something like 73% dark energy, 23% dark matter and then four percent of the ordinary matter. This means that we are in the tail of the distribution. The dark stuff is the normal stuff.”

You started the paper with the analogy of a polymer and introduced the entropic force... so can one say that the whole universe is a stretched spaghetti which wants to curl back into its equilibrium state?
“Well, I wanted to compare normal matter to a little bead attached to the polymer, which is out of equilibrium. That's what ordinary matter is. There is something connecting the matter with the other stuff. So the spaghetti is something that is in between the dark energy and matter itself and may play the role of dark matter itself, because on n end it is attached to the matter. So the thing you take out of equilibrium is really – yeah on particle out of it... but anyhow, the other analogy is similar and could be used also.“

We humans are normally taking space, time and gravity for granted as a priori things, and here you come and tell us that we only have emergent phenomena, like fractals on a sponge or something, and the only basic things are energy, states and probability distributions...
“We know that when we want to combine gravity and quantum mechanics, we have to give up the notion of space and time in some form, and the problem with most theories we have – even string theory – we write down the equations in spacetime. It is very hard to start up with something where you don't have it. Certainly this last year I have been thinking much more about that and I do have a feeling that I am making progress. You're right, after putting out the paper people started to discuss what's different from what Jacobson did, but I didn't even pretend that I have a full theory. I only had an idea, and of course there are some details that you might question. There are many questions it raises instead of answering. But for me those questions are challenges to make it sort of more precise. Some people dismiss it, which I think is really stupid, to be honest, because people how know about this subject should be able to realize that I have captured some important thing. I am not unhappy that some people call it controversial or even wrong. In a certain way it would be much worse for me if they said it is already done and it is trivial.”

“But I have to admit one thing: the people that now have written about my work, are not the people who really understand the issues. So if you ask me: have the right people jumped on it, I would say no. There are a lot of things which have been written, which are totally wrong, and it make me feel a little uneasy about it. Because some people may say, 'well, Verlinde writes some simple equations, I can do that too'. But it is not the same thing. I added an idea, a concept, and I don't think anything really new has been added to my idea. One exception I want to make is what people are doing in the context of cosmology, because I started realizing now that that is really the area where my ideas will make most impact. In that sense it is good that I brought the paper out. Because you do get feedback, and it helps to give me ideas is what direction we need to think.”

Any good theory should be able to predict things and allow falsification. What about that aspect of your idea?
“That's a good question. I think I have it in my conclusion. If you say that gravity is like thermodynamics, then what happens is that the normal thermodynamical laws apply, but statistical mechanics does more. It gives you the fluctuations around it. So it is in the fluctuations where you want to look. Now, in order to see fluctuations it is better to take signals where the leading part is small and the fluctuations large. If you have a very strong signal, the fluctuations are just tiny corrections on the big object. But if you have a tiny signal, the fluctuations can be just as large as the thing you are looking at. So, you want to look at situations where gravity is very very weak. This is the opposite of what people would do in string theory where you would want a very strong signal. It is indeed true that Einstein's general theory of relativity is needed to study very strong gravity, but there is an area there, where we have very weak gravity, and that's cosmology. So I have been calculating these fluctuations and they can be compared to observations. I have observational plots which match exactly my ideas. I cannot make a prediction, because these things were measured already, but there is an agreement with my ideas.”

Can you give an example?
“Yes, it is about dark matter. What people have done is to look at the rotation curves of galaxies. In order to explain them, you have to put a halo of dark matter around it, that's the usual story. And people think then that dark matter is made out of these unobserved particles called wimps. They are particles that are weakly interaction with other mass. It is the most accepted theory. The experiments going on at LHC now are trying to find these particles and maybe explain dark matter.”

“I don't believe it. At least I started to believe that it is not just another particle. As I said, the particles are the stuff which is out of equilibrium. Ordinary matter is just four percent and the rest of it is a completely different dynamics.”

“So what I described in the paper are also some thought experiments that Bekenstein did near the horizons of black holes. What he did – he lowered a box into a black hole – at least as a thought experiment – and that's where he got his equations from, also the thermodynamics of black holes comes from that. Now, he also got bounds on the entropy. Actually the first equation that I have on the change of entropy as a function of the mass, that actually is his equation that he used. But I turned around his logic and got gravity from it.”

“Now what I realized is that the horizons we have near black holes is very much like the horizons we have in cosmology, that is: The horizon of how far we can see. We can turn around the thought experiment and see the galaxies that behave like that. They are the boxes. The horizon that you see in cosmology is like what we have on the outside of a horizon of a black hole. You should think of a horizon in de Sitter space as the horizon of a black hole but with inside out reversed. But the near the horizon dynamics is the same as what you do in cosmology. The point is that black holes have a temperature, just like there is a temperature in cosmology. Now, what I can do is indeed compare that temperature and the number of bits that I think a galaxy should have and calculate what happens. I am currently discussing this with an astronomer and he is providing me with plots that agree with my ideas. ”

An entirely different explanation
"In fact, it is not the same and the modified Newtonian dynamics. I think about it as fluctuations, which is something they didn't think about. So I think I have a theory of what they have been observing phenomenologically. More concrete: If you take the 1/r^2-law of gravity, and look at the centripetal force, which is the velocity squared over the radius, and equate them, then you would know what velocity these objects that rotate at the edges of a galaxy have. And one sees that it happens in a very different way than what one would have gotten from Newton.”

“So, the usual explanation is that we are not seeing enough mass, and that's why they talk about dark matter. But there is another way, and that's to say that the actual law of attraction is somewhat different, or there is another way in which we have to write down the force law. That's actually what people start saying. Instead of F=ma, there is something going like F=ma^2/a_0, where a_0 is the cosmological acceleration and is given as the product of the Hubble constant and the speed of light. I get a similar thing from fluctuations, and it provides a theory for, why it might be so.”

“I havn't added that, but string theory has been around for 40 years, and I think that the predictions of string theory are not that impressive yet. So asking me, after writing a single paper, how to use it for predictions is a bit much.”

Yes, that's true, but it sounds that you already know in which direction to go, namely where gravity is weak and fluctuations are large, so that one could hope to find some experimental or observational verification of your equations.
“Yes, that's right. But my idea is still not developed into something where I can say that I have a theory, but I think I am close to making a next step. And I don't know how many steps are needed. Remember that Einstein took 8 years from the equivalence principle to general relativity, and it took 25 years from Planck to a more or less finished version of quantum mechanics. So you never know."